Burst error correcting codes, such as Fire codes, have traditionally been decoded using Linear Feedback Shift Registers (LFSR). However, such sequential decoding schemes are not suitable for modern ultra high-speed channels that demand high-speed parallel decoding employing only combinational logic circuitry. This paper proposes a parallel decoding method for cyclic burst error correcting codes. Under this method, a binary companion matrix T defines the entire decoding process. Hence, the decoding method can be implemented using only combinational logic.